Three essays on renegotiation in games

The three essays are connected by a common theme: With renegotiation allowed at any stage of a game, players cannot rely on inefficient continuations to support ex ante favorable outcomes. Roughly, strategy profiles which are not subject to this criticism are renegotiation-proof.

There are two different approaches to renegotiation-proofness in the literature: In one renegotiation-moves are fully modeled; and hence the renegotiation-proofness constraint appears as a restriction on the games to be considered. The other approach seeks to refine the set of sequentially rational equilibria in games without explicit pre- and intraplay communication.

The first essay, using the first approach, studies commitment in a durable good bargaining model. The buyer's valuation changes randomly over time. Two scenarios are considered: In one the seller offers the good for sale, in the other she offers renegotiation-proof long-term rental contracts. There are multiple equilibrium outcomes in the sale model but generically only one passes a refinement. It is known that without random valuations the outcome in the sale model coincides with the one with long-term rental contracts. Here however long-term rental contracts outperform selling because they are flexible enough to exploit changing valuations.

The second essay is concerned with the second approach to renegotiation-proofness. Weakly renegotiation-proof theories are defined for nonstationary games. It is shown that weakly renegotiation-proof theories in infinite games can be characterized as limits of approximate weakly renegotiation-proof theories in those games' truncations.

The third essay provides a partial reconciliation of the two approaches. Communication in repeated games is modeled explicitly by introducing intraplay bargaining rounds. Credible strategy profiles are self-enforcing as long as they are not renegotiated and the incentive constraints recognize the possibility of future renegotiation. If profiles with redundant renegotiation are excluded one obtains the set of renegotiation-perfect profiles. Standard solution concepts can then be characterized via assumptions on threat points and bargaining costs. Bargaining costs are shown to play an essential role in supporting incentive-efficient outcomes.